Learning Stability Certificates from Data

Nicholas Boffi, Stephen Tu, Nikolai Matni, Jean-Jacques Slotine, Vikas Sindhwani
Proceedings of the 2020 Conference on Robot Learning, PMLR 155:1341-1350, 2021.

Abstract

Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function which guarantees a desired property. However, algorithms for synthesizing certificate functions typically require a closed-form analytical expression of the underlying dynamics, which rules out their use on many modern robotic platforms. To circumvent this issue, we develop algorithms for learning certificate functions only from trajectory data. We establish bounds on the generalization error – the probability that a certificate will not certify a new, unseen trajectory – when learning from trajectories, and we convert such generalization error bounds into global stability guarantees. We demonstrate empirically that certificates for complex dynamics can be efficiently learned, and that the learned certificates can be used for downstream tasks such as adaptive control.

Cite this Paper

BibTeX
@InProceedings{pmlr-v155-boffi21a, title = {Learning Stability Certificates from Data}, author = {Boffi, Nicholas and Tu, Stephen and Matni, Nikolai and Slotine, Jean-Jacques and Sindhwani, Vikas}, booktitle = {Proceedings of the 2020 Conference on Robot Learning}, pages = {1341--1350}, year = {2021}, editor = {Kober, Jens and Ramos, Fabio and Tomlin, Claire}, volume = {155}, series = {Proceedings of Machine Learning Research}, month = {16--18 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v155/boffi21a/boffi21a.pdf}, url = {https://proceedings.mlr.press/v155/boffi21a.html}, abstract = {Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function which guarantees a desired property. However, algorithms for synthesizing certificate functions typically require a closed-form analytical expression of the underlying dynamics, which rules out their use on many modern robotic platforms. To circumvent this issue, we develop algorithms for learning certificate functions only from trajectory data. We establish bounds on the generalization error – the probability that a certificate will not certify a new, unseen trajectory – when learning from trajectories, and we convert such generalization error bounds into global stability guarantees. We demonstrate empirically that certificates for complex dynamics can be efficiently learned, and that the learned certificates can be used for downstream tasks such as adaptive control.} }
Endnote
%0 Conference Paper %T Learning Stability Certificates from Data %A Nicholas Boffi %A Stephen Tu %A Nikolai Matni %A Jean-Jacques Slotine %A Vikas Sindhwani %B Proceedings of the 2020 Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2021 %E Jens Kober %E Fabio Ramos %E Claire Tomlin %F pmlr-v155-boffi21a %I PMLR %P 1341--1350 %U https://proceedings.mlr.press/v155/boffi21a.html %V 155 %X Many existing tools in nonlinear control theory for establishing stability or safety of a dynamical system can be distilled to the construction of a certificate function which guarantees a desired property. However, algorithms for synthesizing certificate functions typically require a closed-form analytical expression of the underlying dynamics, which rules out their use on many modern robotic platforms. To circumvent this issue, we develop algorithms for learning certificate functions only from trajectory data. We establish bounds on the generalization error – the probability that a certificate will not certify a new, unseen trajectory – when learning from trajectories, and we convert such generalization error bounds into global stability guarantees. We demonstrate empirically that certificates for complex dynamics can be efficiently learned, and that the learned certificates can be used for downstream tasks such as adaptive control.
APA
Boffi, N., Tu, S., Matni, N., Slotine, J. & Sindhwani, V.. (2021). Learning Stability Certificates from Data. Proceedings of the 2020 Conference on Robot Learning, in Proceedings of Machine Learning Research 155:1341-1350 Available from https://proceedings.mlr.press/v155/boffi21a.html.

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